For various high power applications, e.g., UHF television transmission, it is conventional to couple RF power between the transmitter and the antenna through a rigid coaxial transmission line. Further, in some applications, the transmitter may be located a substantial distance from the antenna so that the transmission line is necessarily made up of multiple sections. Conventionally, such multi-section runs are made up of sections which are essentially all of the same length, since this simplifies design and manufacturing. To prevent accumulating interference effects, the length of each section is normally selected so as to not be a multiple of a half wavelength of the frequency corresponding to the channel allocation for the particular television station. In some instances however, an antenna may be operated at a variety of frequencies within a substantial band, and this prior art technique may be ineffective in preventing reflections accumulating to an unacceptable voltage standing wave ratio (VSWR).
The VSWR (numeric ratio) is directly related to the return loss (in dB=20 log10(VSWR+1/VSWR-1) and reflection coefficient (VSWR-1/VSWR+1), and these terms are used interchangeably, with an appropriate change of units.
It is thus well known that discontinuities in a transmission line lead to impedance mismatches and “reflections”. Where the discontinuities are evenly spaced over multiple segments, the effects of the discontinuities may be additive, resulting in significant degradation in performance of certain channels within a broadcast band.
Rigid coaxial transmission line systems are assembled from multiple sections of copper line and appropriate connectors. The connection points do not have the same characteristics as the continuous portions of the copper lines. Practical fabrication methods and physical constraints do not allow for “transparent” couplings, i.e., those which do not affect electromagnetic wave transmission. When equal stock lengths are used in a system, the connection discontinuities add up to produce non-usable portions of the frequency band. More than 70% of the span is unaffected, as the reflections from the discontinuities are selective. Typically, a minimum number of lines may be used without regard before the reflections become a problem.
The primary area where rigid lines are used is terrestrial television and FM radio signals between the transmitter amplifier and antenna mast. When the portion of the frequency band that is affected by connector reflections falls on a particular station's frequency, an alternate stock length is chosen for the system. When many low power stations wish to operate on the same line, levels permitting, more than half the systems can be accommodated with stock line lengths. A special length can be supplied to cover any group of known stations.
The rare time when the station frequencies are unknown, methods of displacing the reflection buildup can be applied. However, there is a price to pay. When systems of common length lines are used, all of the connector reflections appear at fixed positions: with only residual line reflections in band. Any method that distributes the reflections ends up with a complex addition of joint reflections and line discontinuities.
Reflection coefficients greater than 0.05 are known to degrade NTSC (analog television) service, while Bit Error Rates (BER) become a problem on HDTV (High definition Television, digital television). Typical reflection coefficients, for fixed length line systems in operation, are 0.01 to 0.03, while distributed length line systems are 0.03 to 0.05. The small degradation in picture quality is a tradeoff made for the ability to operate multiple stations with complex carrier frequency spacing.
U.S. Pat. No. 5,455,548, expressly incorporated herein, relates to a rigid coaxial transmission line, which seeks to achieve low Vertical Standing Wave Ratio (VSWR) characteristics over a frequency band by providing a “progressive distribution” of line lengths. Therefore, the individual segment line lengths are distributed essentially according to the formula:I=L+(λ(n−1))/(2N) for n=1 to N. 
This formula, thus provides a deterministic formula for a priori defining the line lengths, presuming that an even distribution of impedance discontinuity effects by incremental spacing is optimal. A particular advantage of this type of system is that only the operating wavelength, overall run length and number of segments need be known in order to determine all of the individual line lengths.
Therefore, U.S. Pat. No. 5,455,548, proposes distributing the length of the transmission line segments linearly across a range so that the respective reflections from the ends of each transmission line segment do not superpose with each other causing an increase in VSWR in a particular portion of the band. While the design proposed by U.S. Pat. No. 5,455,548 does indeed reduce the maximum VSWR for any wavelength within the band, as compared to equal length segments, there still exists significant degradation of the transmitted signal.
U.S. Pat. No. 5,719,794, expressly incorporated herein by reference, provides a method for optimizing an antenna using a computerized process for the design of wire antennas using a genetic algorithm in conjunction with an electromagnetic code. The process designs antennas using a completely deductive approach; that is, the desired electromagnetic properties of the antenna are specified and the physical configuration that most closely produces these results is then synthesized. The only constraints on the antenna design are its size and any other relevant constraints (such as materials to use, e.g. thin wires). The genetic algorithm is applied in a multi-step process. In the first step, the electromagnetic properties of the desired antenna are specified. These properties can include, but are not limited to the radiation pattern, frequency range, polarization and input impedance. In the second step, a genetic algorithm and a suitable electromagnetic code are selected. The electromagnetic code computes the resulting antenna prospectives from each wire configuration designated by the genetic algorithm. A cost function is formulated, with or without computer assistance, which will return a single number for a given trial. This number is a figure of merit of the input desired characteristics. The user or computer determines the constraints of the design space (e.g. size, shape, number of design points, maximum lengths of wire, number of wire segments). Some or all of the constraints can be made a part of the genetic string itself. The number of bits to use in the genetic strings and the method of translating the strings into design features/characteristics (e.g. points in space, wire locations, type of feature) are specified, making sure the genetic string will not produce errors that are going to crash the simulation and/or are not accounted for in the cost function. All other genetic algorithm parameters—size of the population, number of generations, etc.—are specified by the user. The process is started and runs to completion as defined by either the computer or user, and the optimum design is output in some form (file, text, etc.) when the program has finished its run.
U.S. Pat. No. 4,831,346, expressly incorporated herein by reference, relates to coaxial transmission lines, for example coaxial cables which are somewhat flexible so that they can be used in installations which require the transmission line to bend. The coaxial cable assembly, o at least the outer conductor thereof, is fabricated and shipped in relatively short lengths (e.g., thirty-nine feet) rather than long lengths wound on reels. These lengths are generally of even length, and are coupled to function like a continuous cable after it has been assembled and installed.
U.S. Pat. No. 5,436,846, expressly incorporated herein by reference, proposes a method for analyzing a microwave system seeking to yield mutually consistent values for the insertion loss and the voltage standing wave ratio or return loss of the system, as well as heat losses, based solely on knowledge of the insertion loss and voltage standing wave ratio performance of the individual constituent components of the system.
U.S. Pat. No. 3,763,445, expressly incorporated herein by reference, discloses a variable length transmission line. U.S. Pat. No. 4,988,961, expressly incorporated herein by reference, provides an antenna coupler for reducing mismatch in an antenna “T” coupler. U.S. Pat. No. 4,019,162, expressly incorporated herein by reference, relates to a Coaxial transmission line with reflection compensation.